Adjoint Matching

Follow this topic Ask about this topic

Recent momentum

emerging

1 papers in the last 28 days · 0.0% of indexed attention

Twelve weeks of publication activity for this topic as it is defined today.

25 papers

Latest in Adjoint Matching

Browse all topics →

A Lagrangian View of Flow Matching
Aug 31, 2026Peyman MilanfarAdjoint Matching Generative Models
Unifying Physical Backpropagation
Aug 12, 2026Cyrill Bösch, Yigithan Gediz, Clara C. Wanjura +1Backpropagation Adjoint Matching
Differentiate the Solver, Not the Equation: Reverse-Sweep Adjoints for Block Implicit Simulation
Aug 9, 2026Lei Shu, Ying Jiang, Kui Wu +3Adjoint Matching Automatic Differentiation
Physics-enhanced reinforcement learning for real-time optimal control of dynamical systems
Jul 17, 2026Matteo Tomasetto, Nicolò Botteghi, Gabriele Bruni +1Iterative Reinforcement Learning Optimal Control
Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstruction
Jul 16, 2026Guixian Xu, Jinglai Li, Junqi TangImage Reconstruction Image Denoising
An AI-Assisted Solution to the Signed BAR Conjecture: Uniqueness in the Harrison--Reiman Class and a Completely- $\mathcal{S}$ Class Obstruction
Jul 3, 2026Yiping Lu, Youheng ZhuAdjoint Matching Automatic Differentiation
Scalable Maximum Entropy Reinforcement Learning for Diffusion Policies via Adjoint Matching
Jun 21, 2026Serge Thilges, Onur Celik, Denis Blessing +2Diffusion Policies Offline Reinforcement Learning
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Jun 10, 2026Zhen Zhang, Alessandro Alla, George Em KarniadakisConventional Physics-Informed Neural Networks Ill-Posed Inverse Problem
Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events
Jun 4, 2026Rishal Aggarwal, David Ryan Koes, Nicholas M. Boffi +1Conditional Flow Matching Reaction
Unsupervised Diffusion Solver for Combinatorial Optimization via Combinatorial Adjoint Matching
May 29, 2026Shengyu Feng, Tarun Suresh, Yiming YangCombinatorial Optimization Adjoint Matching
Trust Region Q Adjoint Matching
May 26, 2026Yonghoon Dong, Kyungmin Lee, Changyeon Kim +2Flow-Based Policy Off-Policy Evaluation
Vocabulary-size-independent Convergence of Discrete Diffusion Models: adjoint equations induce the right space
May 17, 2026Kelvin Kan, Xingjian Li, Benjamin J. Zhang +3Discrete Diffusion Model Generative Models
Efficient Adjoint Matching for Fine-tuning Diffusion Models
May 12, 2026Jeongwoo Shin, Dongsoo Shin, Yuchen Zhu +5Adjoint Matching Reward Gradients
Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models
May 11, 2026Andreas Bergmeister, Stefanie Jegelka, Nikolas Nüsken +2Reinforcement Learning Post-Training Reward Gradients
Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline
May 7, 2026Zhengyi Guo, Jiayuan Sheng, David D. Yao +1Generative Flow Networks Adjoint Matching
SNAPO: Smooth Neural Adjoint Policy Optimization for Optimal Control via Differentiable Simulation
May 7, 2026Dmitri Goloubentsev, Natalija KarpichinaMulti-Objective Policy Optimization Adjoint Matching
Entropy-Regularized Adjoint Matching for Offline Reinforcement Learning
May 7, 2026Abdelghani Ghanem, Mounir GhoghoOffline Reinforcement Learning Flow-Based Policy
Neural Control: Adjoint Learning Through Equilibrium Constraints
May 5, 2026Dezhong Tong, Jiawen Wang, Hengyi Zhou +3Neural Control Neural Ordinary Differential Equations
Calibration of the underlying surface parameters for urban flood using latent variables and adjoint equation
May 3, 2026Yongfu Tian, Shan Ding, Guofeng Su +1Sen1Floods11 Surrogate Models
A unified perspective on fine-tuning and sampling with diffusion and flow models
Apr 30, 2026Carles Domingo-Enrich, Yuanqi Du, Michael S. AlbergoAdjoint Matching Generative Models
Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schrödinger Bridge Problem
Apr 25, 2026Georgiy A. Bondar, Asmaa Eldesoukey, Yongxin Chen +1Schrödinger Bridges Sinkhorn
Generative Flow Networks for Model Adaptation in Digital Twins of Natural Systems
Apr 22, 2026Pascal Archambault, Houari Sahraoui, Eugene SyrianiDigital Twins Parameter-Efficient Adaptation
Neural Adjoint Method for Meta-optics: Accelerating Volumetric Inverse Design via Fourier Neural Operators
Apr 19, 2026Chanik Kang, Hyewon Suk, Haejun ChungGenerative Inverse Design Fourier Neural Operators
Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control
Mar 28, 2026Carles Domingo-Enrich, Jiequn HanAdjoint Matching Stochastic Optimal Control
Counterfactual Operator Relevance for PDE Discovery: Screening, Pruning, and Identifiability
Jun 25, 2025Ronald KatendePartial Differential Equations Identifiability

Aug 31, 2026 · cs.CVJ/K move · Enter open · S save

A Lagrangian View of Flow Matching

Peyman Milanfar

1Google

Modern explicit-time generative models, such as Flow Matching [Lipman et al., 2023] and Rectified Flow [Liu et al., 2023], are typically derived top-down via Optimal Transport and the continuity equation. This standard Eulerian approach focuses on the macroscopic transport of probability mass. In this paper, we present an alternative, bottom-up mechanical derivation grounded in a Lagrangian (particle-centric) perspective. By analyzing the local Taylor expansion of a continuous denoiser, we motivate a strict invariance condition required for optimal, singlestep generation: the conservation of target identity. Enforcing this condition yields a governing quasi-linear advection Partial Differential Equation (PDE). We demonstrate that solving this PDE via the Method of Characteristics analytically yields the straight-line trajectories of Flow Matching. This geometric perspective isolates the Jacobian of the denoiser as the primary source of trajectory curvature, providing a direct mathematical explanation for why straight-line flows enable massive step sizes, and why empirical models require distillation to flatten intersecting characteristics.

Adjoint Matching Generative Models Lagrangian Methods Few-Step Generation Mechanical Systems

Open paper Ask about it PDF